Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.383");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 306 x^{18} + 37827 x^{16} + 2442168 x^{14} + 88368509 x^{12} + 1774000974 x^{10} + \cdots + 2870280625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{88}\cdot 3^{14}\cdot 41^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.1 | ||
Root | \(7.62048i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.6.c.a.383.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −15.4378 | − | 2.16198i | −0.990336 | − | 0.138691i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 81.6092i | 1.45987i | 0.683517 | + | 0.729934i | \(0.260449\pi\) | ||||
−0.683517 | + | 0.729934i | \(0.739551\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 91.7503i | 0.707721i | 0.935298 | + | 0.353861i | \(0.115131\pi\) | ||||
−0.935298 | + | 0.353861i | \(0.884869\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 233.652 | + | 66.7525i | 0.961530 | + | 0.274702i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −710.534 | −1.77053 | −0.885265 | − | 0.465088i | \(-0.846023\pi\) | ||||
−0.885265 | + | 0.465088i | \(0.846023\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −666.057 | −1.09308 | −0.546541 | − | 0.837432i | \(-0.684056\pi\) | ||||
−0.546541 | + | 0.837432i | \(0.684056\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 176.438 | − | 1259.87i | 0.202471 | − | 1.44576i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2172.09i | 1.82287i | 0.411449 | + | 0.911433i | \(0.365023\pi\) | ||||
−0.411449 | + | 0.911433i | \(0.634977\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1126.10i | 0.715640i | 0.933791 | + | 0.357820i | \(0.116480\pi\) | ||||
−0.933791 | + | 0.357820i | \(0.883520\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 198.362 | − | 1416.42i | 0.0981547 | − | 0.700882i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3120.07 | −1.22983 | −0.614914 | − | 0.788594i | \(-0.710809\pi\) | ||||
−0.614914 | + | 0.788594i | \(0.710809\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3535.05 | −1.13122 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3462.75 | − | 1535.66i | −0.914138 | − | 0.405403i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 371.221i | − | 0.0819666i | −0.999160 | − | 0.0409833i | \(-0.986951\pi\) | ||
0.999160 | − | 0.0409833i | \(-0.0130490\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2506.88i | 0.468520i | 0.972174 | + | 0.234260i | \(0.0752668\pi\) | ||||
−0.972174 | + | 0.234260i | \(0.924733\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10969.1 | + | 1536.16i | 1.75342 | + | 0.245557i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7487.66 | −1.03318 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6270.56 | 0.753013 | 0.376506 | − | 0.926414i | \(-0.377125\pi\) | ||||
0.376506 | + | 0.926414i | \(0.377125\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10282.5 | + | 1440.00i | 1.08252 | + | 0.151601i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15413.6i | 1.43200i | 0.698098 | + | 0.716002i | \(0.254030\pi\) | ||||
−0.698098 | + | 0.716002i | \(0.745970\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11515.9i | 0.949786i | 0.880044 | + | 0.474893i | \(0.157513\pi\) | ||||
−0.880044 | + | 0.474893i | \(0.842487\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5447.62 | + | 19068.1i | −0.401028 | + | 1.40371i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 21034.7 | 1.38896 | 0.694482 | − | 0.719510i | \(-0.255634\pi\) | ||||
0.694482 | + | 0.719510i | \(0.255634\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8388.89 | 0.499131 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4696.01 | − | 33532.2i | 0.252815 | − | 1.80525i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 23609.2i | 1.15450i | 0.816569 | + | 0.577248i | \(0.195873\pi\) | ||||
−0.816569 | + | 0.577248i | \(0.804127\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 57986.1i | − | 2.58474i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2434.62 | − | 17384.6i | 0.0992529 | − | 0.708724i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4375.95 | −0.163660 | −0.0818300 | − | 0.996646i | \(-0.526076\pi\) | ||||
−0.0818300 | + | 0.996646i | \(0.526076\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −53029.6 | −1.82471 | −0.912355 | − | 0.409399i | \(-0.865738\pi\) | ||||
−0.912355 | + | 0.409399i | \(0.865738\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6124.56 | + | 21437.6i | −0.194412 | + | 0.680495i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 54356.3i | − | 1.59576i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 24727.7i | − | 0.672971i | −0.941689 | − | 0.336485i | \(-0.890762\pi\) | ||
0.941689 | − | 0.336485i | \(-0.109238\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 48167.0 | + | 6745.53i | 1.21794 | + | 0.170566i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −27045.3 | −0.636717 | −0.318359 | − | 0.947970i | \(-0.603132\pi\) | ||||
−0.318359 | + | 0.947970i | \(0.603132\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15536.8 | 0.341236 | 0.170618 | − | 0.985337i | \(-0.445424\pi\) | ||||
0.170618 | + | 0.985337i | \(0.445424\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 54573.5 | + | 7642.72i | 1.12028 | + | 0.156890i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 65191.7i | − | 1.25304i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 42768.6i | − | 0.771005i | −0.922707 | − | 0.385503i | \(-0.874028\pi\) | ||
0.922707 | − | 0.385503i | \(-0.125972\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 50137.2 | + | 31193.7i | 0.849078 | + | 0.528268i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 29099.1 | 0.463644 | 0.231822 | − | 0.972758i | \(-0.425531\pi\) | ||||
0.231822 | + | 0.972758i | \(0.425531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −177262. | −2.66115 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −802.572 | + | 5730.83i | −0.0113681 | + | 0.0811745i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18718.0i | 0.250487i | 0.992126 | + | 0.125243i | \(0.0399711\pi\) | ||||
−0.992126 | + | 0.125243i | \(0.960029\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 61110.9i | − | 0.773598i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5419.82 | − | 38700.7i | 0.0649797 | − | 0.463993i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −91900.4 | −1.04474 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14698.6 | −0.158615 | −0.0793077 | − | 0.996850i | \(-0.525271\pi\) | ||||
−0.0793077 | + | 0.996850i | \(0.525271\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −166017. | − | 47429.9i | −1.70242 | − | 0.486367i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 27203.5i | − | 0.265352i | −0.991159 | − | 0.132676i | \(-0.957643\pi\) | ||
0.991159 | − | 0.132676i | \(-0.0423569\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 138397.i | − | 1.28539i | −0.766124 | − | 0.642693i | \(-0.777817\pi\) | ||
0.766124 | − | 0.642693i | \(-0.222183\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 115593. | + | 16188.2i | 1.02320 | + | 0.143293i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −48368.3 | −0.408414 | −0.204207 | − | 0.978928i | \(-0.565462\pi\) | ||||
−0.204207 | + | 0.978928i | \(0.565462\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3391.57 | 0.0273423 | 0.0136711 | − | 0.999907i | \(-0.495648\pi\) | ||||
0.0136711 | + | 0.999907i | \(0.495648\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −96803.7 | − | 13556.8i | −0.745735 | − | 0.104436i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 56024.3i | − | 0.412744i | −0.978474 | − | 0.206372i | \(-0.933834\pi\) | ||
0.978474 | − | 0.206372i | \(-0.0661656\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 254626.i | − | 1.79539i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −155625. | − | 44461.0i | −1.05103 | − | 0.300272i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −199289. | −1.29008 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 343808. | 2.13477 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 33323.9 | − | 237952.i | 0.198606 | − | 1.41816i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 33464.2i | − | 0.191560i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 58547.1i | − | 0.322104i | −0.986946 | − | 0.161052i | \(-0.948511\pi\) | ||
0.986946 | − | 0.161052i | \(-0.0514887\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24897.1 | − | 177780.i | 0.131727 | − | 0.940607i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 343480. | 1.74873 | 0.874367 | − | 0.485265i | \(-0.161277\pi\) | ||||
0.874367 | + | 0.485265i | \(0.161277\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −103320. | −0.506473 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 125324. | − | 282592.i | 0.591835 | − | 1.33452i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 123940.i | − | 0.564170i | −0.959389 | − | 0.282085i | \(-0.908974\pi\) | ||
0.959389 | − | 0.282085i | \(-0.0910260\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 178910.i | 0.785411i | 0.919664 | + | 0.392705i | \(0.128461\pi\) | ||||
−0.919664 | + | 0.392705i | \(0.871539\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −324729. | − | 45476.5i | −1.37554 | − | 0.192637i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 473256. | 1.93533 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30295.0 | 0.119661 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −129506. | − | 18136.6i | −0.494307 | − | 0.0692250i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 465521.i | 1.71781i | 0.512139 | + | 0.858903i | \(0.328853\pi\) | ||||
−0.512139 | + | 0.858903i | \(0.671147\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 81121.6i | 0.289531i | 0.989466 | + | 0.144765i | \(0.0462427\pi\) | ||||
−0.989466 | + | 0.144765i | \(0.953757\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −144992. | + | 507512.i | −0.500744 | + | 1.75274i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −204584. | −0.683978 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 106710. | 0.345506 | 0.172753 | − | 0.984965i | \(-0.444734\pi\) | ||||
0.172753 | + | 0.984965i | \(0.444734\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 51042.7 | − | 364475.i | 0.160118 | − | 1.14334i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 286267.i | − | 0.870376i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15721.2i | 0.0463466i | 0.999731 | + | 0.0231733i | \(0.00737695\pi\) | ||||
−0.999731 | + | 0.0231733i | \(0.992623\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −125365. | + | 895178.i | −0.358481 | + | 2.55976i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5039.69 | −0.0139834 | −0.00699170 | − | 0.999976i | \(-0.502226\pi\) | ||||
−0.00699170 | + | 0.999976i | \(0.502226\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 72338.7 | 0.194829 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −75170.3 | + | 263116.i | −0.196587 | + | 0.688109i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 177743.i | − | 0.451520i | −0.974183 | − | 0.225760i | \(-0.927514\pi\) | ||
0.974183 | − | 0.225760i | \(-0.0724865\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 324342.i | − | 0.800587i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 67555.1 | + | 9460.73i | 0.162078 | + | 0.0226982i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −240296. | −0.560550 | −0.280275 | − | 0.959920i | \(-0.590426\pi\) | ||||
−0.280275 | + | 0.959920i | \(0.590426\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 572922. | 1.29987 | 0.649933 | − | 0.759991i | \(-0.274797\pi\) | ||||
0.649933 | + | 0.759991i | \(0.274797\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 818661. | + | 114649.i | 1.80708 | + | 0.253071i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 511735.i | 1.09930i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.54334e6i | − | 3.22744i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 140897. | − | 317708.i | 0.286912 | − | 0.646955i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −342586. | −0.679494 | −0.339747 | − | 0.940517i | \(-0.610341\pi\) | ||||
−0.339747 | + | 0.940517i | \(0.610341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 782820. | 1.51275 | 0.756377 | − | 0.654136i | \(-0.226967\pi\) | ||||
0.756377 | + | 0.654136i | \(0.226967\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −117517. | + | 839143.i | −0.221317 | + | 1.58034i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 548639.i | − | 1.00721i | −0.863933 | − | 0.503606i | \(-0.832006\pi\) | ||
0.863933 | − | 0.503606i | \(-0.167994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 626664.i | 1.12177i | 0.827895 | + | 0.560883i | \(0.189538\pi\) | ||||
−0.827895 | + | 0.560883i | \(0.810462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −53460.8 | + | 381741.i | −0.0933351 | + | 0.666467i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 34059.6 | 0.0580095 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.25789e6 | −2.09054 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −729009. | − | 208272.i | −1.18252 | − | 0.337836i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 800135.i | − | 1.26706i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 291994.i | 0.451511i | 0.974184 | + | 0.225755i | \(0.0724850\pi\) | ||||
−0.974184 | + | 0.225755i | \(0.927515\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 417521. | + | 58471.5i | 0.630564 | + | 0.0883071i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −939801. | −1.38656 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −230006. | −0.331582 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −239854. | − | 33590.3i | −0.337938 | − | 0.0473264i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.44673e6i | − | 1.99254i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 314665.i | 0.423727i | 0.977299 | + | 0.211864i | \(0.0679533\pi\) | ||||
−0.977299 | + | 0.211864i | \(0.932047\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −825971. | − | 235974.i | −1.08770 | − | 0.310747i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 446955. | 0.575704 | 0.287852 | − | 0.957675i | \(-0.407059\pi\) | ||||
0.287852 | + | 0.957675i | \(0.407059\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 522511. | 0.658426 | 0.329213 | − | 0.944256i | \(-0.393217\pi\) | ||||
0.329213 | + | 0.944256i | \(0.393217\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −140943. | + | 1.00642e6i | −0.173786 | + | 1.24093i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.06954e6i | 1.29064i | 0.763911 | + | 0.645321i | \(0.223276\pi\) | ||||
−0.763911 | + | 0.645321i | \(0.776724\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.71662e6i | 2.02770i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −92465.0 | + | 660253.i | −0.106932 | + | 0.763554i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.08235e6 | −1.22567 | −0.612837 | − | 0.790209i | \(-0.709972\pi\) | ||||
−0.612837 | + | 0.790209i | \(0.709972\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −372598. | −0.413235 | −0.206618 | − | 0.978422i | \(-0.566246\pi\) | ||||
−0.206618 | + | 0.978422i | \(0.566246\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −706568. | − | 589958.i | −0.767606 | − | 0.640922i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 684610.i | 0.728665i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 750049.i | − | 0.782253i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −449227. | − | 62911.8i | −0.459163 | − | 0.0643034i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 888643. | 0.890314 | 0.445157 | − | 0.895453i | \(-0.353148\pi\) | ||||
0.445157 | + | 0.895453i | \(0.353148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.21692e6 | 2.17745 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.73654e6 | + | 383237.i | 2.63543 | + | 0.369077i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.28879e6i | − | 1.21716i | −0.793492 | − | 0.608581i | \(-0.791739\pi\) | ||
0.793492 | − | 0.608581i | \(-0.208261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 575326.i | 0.532923i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24779.9 | − | 86736.3i | 0.0225164 | − | 0.0788133i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 572092. | 0.510007 | 0.255004 | − | 0.966940i | \(-0.417923\pi\) | ||||
0.255004 | + | 0.966940i | \(0.417923\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.92673e6 | −1.68541 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 40468.0 | − | 288965.i | 0.0347403 | − | 0.248066i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2.32783e6i | − | 1.96142i | −0.195467 | − | 0.980710i | \(-0.562622\pi\) | ||
0.195467 | − | 0.980710i | \(-0.437378\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.15421e6i | 1.78182i | 0.454177 | + | 0.890912i | \(0.349934\pi\) | ||||
−0.454177 | + | 0.890912i | \(0.650066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −132121. | + | 943418.i | −0.107291 | + | 0.766121i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.51178e6 | 2.00285 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −473172. | −0.370526 | −0.185263 | − | 0.982689i | \(-0.559314\pi\) | ||||
−0.185263 | + | 0.982689i | \(0.559314\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −167340. | + | 585736.i | −0.128703 | + | 0.450496i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.42241e6i | − | 1.07463i | −0.843381 | − | 0.537315i | \(-0.819439\pi\) | ||
0.843381 | − | 0.537315i | \(-0.180561\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.03901e6i | 1.51340i | 0.653764 | + | 0.756698i | \(0.273189\pi\) | ||||
−0.653764 | + | 0.756698i | \(0.726811\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.41874e6 | + | 198687.i | 1.03464 | + | 0.144896i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.41420e6 | −1.01346 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.29810e6 | −2.32284 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 226914. | + | 31778.0i | 0.157083 | + | 0.0219986i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.17933e6i | 1.48304i | 0.670930 | + | 0.741521i | \(0.265895\pi\) | ||||
−0.670930 | + | 0.741521i | \(0.734105\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 357118.i | − | 0.238922i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.46040e6 | + | 1.09114e6i | 1.61851 | + | 0.717777i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.07814e6 | 1.34430 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.05658e6 | −0.672184 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −58813.6 | + | 419963.i | −0.0368020 | + | 0.262787i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 4.32770e6i | − | 2.66384i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 695268.i | 0.421024i | 0.977591 | + | 0.210512i | \(0.0675131\pi\) | ||||
−0.977591 | + | 0.210512i | \(0.932487\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −299212. | + | 2.13654e6i | −0.178272 | + | 1.27296i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12139.6 | −0.00711713 | −0.00355857 | − | 0.999994i | \(-0.501133\pi\) | ||||
−0.00355857 | + | 0.999994i | \(0.501133\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 509977. | 0.294232 | 0.147116 | − | 0.989119i | \(-0.453001\pi\) | ||||
0.147116 | + | 0.989119i | \(0.453001\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.74950e6 | − | 499820.i | −0.993433 | − | 0.283816i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.95242e6i | − | 1.09125i | −0.838028 | − | 0.545627i | \(-0.816292\pi\) | ||
0.838028 | − | 0.545627i | \(-0.183708\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 263765.i | 0.145124i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 746700. | + | 104571.i | 0.404467 | + | 0.0566435i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.44599e6 | −1.30452 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.35455e6 | 1.23651 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −52358.4 | − | 7332.52i | −0.0270780 | − | 0.00379214i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.92994e6i | 0.982999i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.46773e6i | 0.736337i | 0.929759 | + | 0.368168i | \(0.120015\pi\) | ||||
−0.929759 | + | 0.368168i | \(0.879985\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.46513e6 | + | 418576.i | 0.724044 | + | 0.206854i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.01800e6 | 0.982449 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.60707e6 | −1.25048 | −0.625241 | − | 0.780432i | \(-0.714999\pi\) | ||||
−0.625241 | + | 0.780432i | \(0.714999\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −121124. | + | 864892.i | −0.0572439 | + | 0.408755i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.78122e6i | − | 0.829529i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.31173e6i | 1.06097i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −550497. | + | 3.93087e6i | −0.249005 | + | 1.77804i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 568898. | 0.253636 | 0.126818 | − | 0.991926i | \(-0.459524\pi\) | ||||
0.126818 | + | 0.991926i | \(0.459524\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.85024e6 | 0.813140 | 0.406570 | − | 0.913620i | \(-0.366725\pi\) | ||||
0.406570 | + | 0.913620i | \(0.366725\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.30639e6 | + | 1.02284e6i | 0.999228 | + | 0.443138i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.50974e6i | 1.49913i | 0.661933 | + | 0.749563i | \(0.269736\pi\) | ||||
−0.661933 | + | 0.749563i | \(0.730264\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2.20715e6i | − | 0.929524i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.07659e6 | + | 430860.i | 1.27761 | + | 0.178923i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 429267. | 0.175789 | 0.0878944 | − | 0.996130i | \(-0.471986\pi\) | ||||
0.0878944 | + | 0.996130i | \(0.471986\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.20799e6 | 0.487860 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.30763e6 | − | 743306.i | −2.11414 | − | 0.296074i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.26795e6i | 0.498160i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 127386.i | 0.0493691i | 0.999695 | + | 0.0246846i | \(0.00785814\pi\) | ||||
−0.999695 | + | 0.0246846i | \(0.992142\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.02890e6 | + | 3.60141e6i | −0.393374 | + | 1.37691i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.16615e6 | −0.817061 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.94120e6 | −1.46675 | −0.733375 | − | 0.679825i | \(-0.762056\pi\) | ||||
−0.733375 | + | 0.679825i | \(0.762056\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −72349.0 | + | 516614.i | −0.0265677 | + | 0.189709i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 247254.i | 0.0895963i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.33847e6i | 1.55145i | 0.631069 | + | 0.775726i | \(0.282616\pi\) | ||||
−0.631069 | + | 0.775726i | \(0.717384\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −126578. | + | 903838.i | −0.0446730 | + | 0.318991i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.67132e6 | −1.27887 | −0.639433 | − | 0.768847i | \(-0.720831\pi\) | ||||
−0.639433 | + | 0.768847i | \(0.720831\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.32024e6 | 1.82928 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −768713. | + | 2.69070e6i | −0.260908 | + | 0.913247i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.46691e6i | − | 1.16163i | −0.814035 | − | 0.580816i | \(-0.802734\pi\) | ||
0.814035 | − | 0.580816i | \(-0.197266\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.77706e6i | − | 2.24181i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.30258e6 | − | 742598.i | −1.73183 | − | 0.242534i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.49031e6 | 1.12557 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.70987e6 | −0.544487 | −0.272244 | − | 0.962228i | \(-0.587766\pi\) | ||||
−0.272244 | + | 0.962228i | \(0.587766\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.59504e6 | + | 223377.i | 0.501579 | + | 0.0702434i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.72203e6i | − | 0.845340i | −0.906284 | − | 0.422670i | \(-0.861093\pi\) | ||
0.906284 | − | 0.422670i | \(-0.138907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.66972e6i | − | 0.512131i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.54569e6 | + | 4.09165e6i | −0.771201 | + | 1.23954i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.45545e6 | −1.33323 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.55419e6 | −0.459405 | −0.229702 | − | 0.973261i | \(-0.573775\pi\) | ||||
−0.229702 | + | 0.973261i | \(0.573775\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −267956. | + | 1.91336e6i | −0.0782454 | + | 0.558717i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 401495.i | − | 0.115826i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.37476e6i | 0.676860i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 386800. | − | 2.76197e6i | 0.108930 | − | 0.777820i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.75545e6 | 0.766756 | 0.383378 | − | 0.923592i | \(-0.374761\pi\) | ||||
0.383378 | + | 0.923592i | \(0.374761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.16875e6 | 0.871329 | 0.435665 | − | 0.900109i | \(-0.356513\pi\) | ||||
0.435665 | + | 0.900109i | \(0.356513\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.91478e6 | + | 1.40412e6i | 1.33553 | + | 0.381551i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 7.67844e6i | − | 2.06206i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 4.86548e6i | − | 1.29139i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.30603e6 | − | 1.02317e6i | −1.91663 | − | 0.268414i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.51741e6 | −1.43068 | −0.715339 | − | 0.698778i | \(-0.753728\pi\) | ||||
−0.715339 | + | 0.698778i | \(0.753728\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.72171e6 | 1.46658 | 0.733290 | − | 0.679916i | \(-0.237984\pi\) | ||||
0.733290 | + | 0.679916i | \(0.237984\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −467688. | − | 65497.2i | −0.118504 | − | 0.0165959i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 3.51352e6i | − | 0.880115i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.22530e6i | − | 0.798747i | −0.916788 | − | 0.399373i | \(-0.869228\pi\) | ||
0.916788 | − | 0.399373i | \(-0.130772\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.96008e6 | + | 559979.i | 0.479929 | + | 0.137112i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.40747e6 | 1.30913 | 0.654567 | − | 0.756004i | \(-0.272851\pi\) | ||||
0.654567 | + | 0.756004i | \(0.272851\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.52756e6 | −0.365678 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.00645e6 | − | 7.18663e6i | 0.238244 | − | 1.70120i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.02319e6i | 0.941792i | 0.882189 | + | 0.470896i | \(0.156069\pi\) | ||||
−0.882189 | + | 0.470896i | \(0.843931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.09519e7i | − | 2.53541i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 175384. | − | 1.25234e6i | 0.0401553 | − | 0.286732i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.98721e6 | 1.12935 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.00035e6 | 0.896000 | 0.448000 | − | 0.894034i | \(-0.352137\pi\) | ||||
0.448000 | + | 0.894034i | \(0.352137\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.33559e6 | − | 7.52139e6i | 0.738994 | − | 1.66635i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.80933e6i | 1.27313i | 0.771222 | + | 0.636567i | \(0.219646\pi\) | ||||
−0.771222 | + | 0.636567i | \(0.780354\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.00938e6i | 0.218828i | 0.993996 | + | 0.109414i | \(0.0348974\pi\) | ||||
−0.993996 | + | 0.109414i | \(0.965103\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.15833e6 | + | 442307.i | 0.677368 | + | 0.0948618i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.13001e6 | 0.239766 | 0.119883 | − | 0.992788i | \(-0.461748\pi\) | ||||
0.119883 | + | 0.992788i | \(0.461748\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.26877e6 | 0.476275 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.64737e6 | − | 230705.i | −0.342167 | − | 0.0479186i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 8.18242e6i | − | 1.68162i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.98084e6i | − | 0.809544i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.57598e6 | + | 5.51634e6i | −0.317142 | + | 1.11008i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.14181e6 | 0.426522 | 0.213261 | − | 0.976995i | \(-0.431591\pi\) | ||||
0.213261 | + | 0.976995i | \(0.431591\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.17655e6 | −0.823105 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −618904. | + | 4.41934e6i | −0.120713 | + | 0.861964i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.19954e6i | − | 0.231558i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.73961e6i | 1.47876i | 0.673290 | + | 0.739378i | \(0.264880\pi\) | ||||
−0.673290 | + | 0.739378i | \(0.735120\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 33989.0 | − | 242701.i | 0.00642786 | − | 0.0458987i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.02474e6 | −1.50220 | −0.751099 | − | 0.660190i | \(-0.770476\pi\) | ||||
−0.751099 | + | 0.660190i | \(0.770476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 806323. | 0.149414 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.87072e6 | − | 1.35485e7i | 0.710033 | − | 2.48530i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 2.48142e6i | − | 0.450618i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.08779e6i | 1.63383i | 0.576757 | + | 0.816916i | \(0.304318\pi\) | ||||
−0.576757 | + | 0.816916i | \(0.695682\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 77801.7 | + | 10895.7i | 0.0138483 | + | 0.00193937i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.15721e6 | −1.61378 | −0.806888 | − | 0.590705i | \(-0.798850\pi\) | ||||
−0.806888 | + | 0.590705i | \(0.798850\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.22006e6 | 0.387379 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.11675e6 | − | 156395.i | −0.192946 | − | 0.0270211i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 6.77792e6i | − | 1.15958i | −0.814765 | − | 0.579792i | \(-0.803134\pi\) | ||
0.814765 | − | 0.579792i | \(-0.196866\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.42551e6i | 0.241500i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.72932e6 | − | 3.89942e6i | 0.290122 | − | 0.654194i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.12945e7 | 1.87649 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.49458e7 | −2.45920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −384277. | + | 2.74396e6i | −0.0626218 | + | 0.447156i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.57819e6i | 0.738924i | 0.929246 | + | 0.369462i | \(0.120458\pi\) | ||||
−0.929246 | + | 0.369462i | \(0.879542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8.98245e6i | − | 1.43595i | −0.696067 | − | 0.717977i | \(-0.745068\pi\) | ||
0.696067 | − | 0.717977i | \(-0.254932\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −701222. | + | 5.00713e6i | −0.111034 | + | 0.792849i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.44515e6 | −0.854050 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.29849e6 | 0.512479 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.02245e6 | − | 292106.i | −0.157364 | − | 0.0449577i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.02663e7i | − | 1.56530i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3.94729e6i | − | 0.596232i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.70965e6 | + | 519516.i | 0.555133 | + | 0.0777434i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.96059e6 | −0.883726 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.25763e6 | 0.184739 | 0.0923697 | − | 0.995725i | \(-0.470556\pi\) | ||||
0.0923697 | + | 0.995725i | \(0.470556\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.84465e6 | − | 1.23865e6i | −1.28730 | − | 0.180280i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 276783.i | 0.0399162i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.63358e6i | − | 0.376338i | −0.982137 | − | 0.188169i | \(-0.939745\pi\) | ||
0.982137 | − | 0.188169i | \(-0.0602553\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.23905e7 | − | 3.53986e6i | −1.75451 | − | 0.501251i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 418033. | 0.0586586 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.92403e6 | 0.545657 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.10636e6 | − | 7.90007e6i | 0.152463 | − | 1.08868i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 3.67084e6i | − | 0.501334i | −0.968073 | − | 0.250667i | \(-0.919350\pi\) | ||
0.968073 | − | 0.250667i | \(-0.0806500\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.67022e6i | − | 1.03819i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.33668e6 | + | 2.38258e7i | −0.447617 | + | 3.19625i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −337916. | −0.0449302 | −0.0224651 | − | 0.999748i | \(-0.507151\pi\) | ||||
−0.0224651 | + | 0.999748i | \(0.507151\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.57210e6 | 0.602552 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.86203e6 | + | 4.60010e6i | −0.373866 | + | 0.600910i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 5.56446e6i | − | 0.720514i | −0.932853 | − | 0.360257i | \(-0.882689\pi\) | ||
0.932853 | − | 0.360257i | \(-0.117311\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.29060e7i | 1.65654i | 0.560331 | + | 0.828269i | \(0.310674\pi\) | ||||
−0.560331 | + | 0.828269i | \(0.689326\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.28877e6 | + | 740664.i | 0.672927 | + | 0.0942398i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.10296e7 | 1.39120 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.16281e6 | 0.520531 | 0.260266 | − | 0.965537i | \(-0.416190\pi\) | ||||
0.260266 | + | 0.965537i | \(0.416190\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.20850e7 | − | 1.69244e6i | −1.49813 | − | 0.209806i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.66985e6i | 0.328131i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.67752e7i | − | 2.04407i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.62842e6 | − | 1.27004e7i | 0.438357 | − | 1.53437i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.04823e6 | −0.724492 | −0.362246 | − | 0.932083i | \(-0.617990\pi\) | ||||
−0.362246 | + | 0.932083i | \(0.617990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.82300e6 | −0.335292 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.18615e6 | + | 8.46978e6i | −0.139691 | + | 0.997478i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.92156e6i | 0.925069i | 0.886601 | + | 0.462534i | \(0.153060\pi\) | ||||
−0.886601 | + | 0.462534i | \(0.846940\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.62638e7i | − | 1.88335i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.35484e6 | − | 9.67432e6i | 0.155579 | − | 1.11092i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.14090e6 | −0.357673 | −0.178837 | − | 0.983879i | \(-0.557233\pi\) | ||||
−0.178837 | + | 0.983879i | \(0.557233\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.13195e6 | 0.127832 | 0.0639161 | − | 0.997955i | \(-0.479641\pi\) | ||||
0.0639161 | + | 0.997955i | \(0.479641\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.65063e6 | − | 5.77766e6i | 0.184866 | − | 0.647081i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.80578e7i | 3.11649i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 4.91816e6i | − | 0.541790i | −0.962609 | − | 0.270895i | \(-0.912680\pi\) | ||
0.962609 | − | 0.270895i | \(-0.0873195\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −525805. | − | 73636.2i | −0.0574489 | − | 0.00804541i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.40103e7 | −1.51825 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.34835e6 | −0.789839 | −0.394920 | − | 0.918716i | \(-0.629228\pi\) | ||||
−0.394920 | + | 0.918716i | \(0.629228\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.94191e7 | + | 2.71954e6i | 2.07033 | + | 0.289939i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.88590e6i | 0.305189i | 0.988289 | + | 0.152594i | \(0.0487628\pi\) | ||||
−0.988289 | + | 0.152594i | \(0.951237\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.44988e7i | 1.52091i | 0.649389 | + | 0.760456i | \(0.275025\pi\) | ||||
−0.649389 | + | 0.760456i | \(0.724975\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.08040e7 | + | 4.79138e6i | 1.12423 | + | 0.498576i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.71738e6 | −0.177275 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.31606e6 | −0.851565 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.72988e6 | + | 1.23523e7i | −0.175730 | + | 1.25482i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.36202e7i | 1.37264i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.30715e7i | − | 1.30693i | −0.756956 | − | 0.653465i | \(-0.773315\pi\) | ||
0.756956 | − | 0.653465i | \(-0.226685\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 631286. | − | 4.50775e6i | 0.0626206 | − | 0.447147i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.77798e6 | 0.470229 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.58748e6 | −0.545591 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.31919e6 | − | 1.80534e6i | −0.612222 | − | 0.174907i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.76946e7i | 1.70096i | 0.526004 | + | 0.850482i | \(0.323690\pi\) | ||||
−0.526004 | + | 0.850482i | \(0.676310\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.17000e6i | 0.302365i | 0.988506 | + | 0.151182i | \(0.0483081\pi\) | ||||
−0.988506 | + | 0.151182i | \(0.951692\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.45085e7 | + | 2.03183e6i | 1.37316 | + | 0.192304i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.04323e7 | 0.979756 | 0.489878 | − | 0.871791i | \(-0.337041\pi\) | ||||
0.489878 | + | 0.871791i | \(0.337041\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.10926e6 | 0.289765 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.55080e6 | + | 497270.i | 0.328377 | + | 0.0459875i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.86705e6i | 0.263119i | 0.991308 | + | 0.131559i | \(0.0419984\pi\) | ||||
−0.991308 | + | 0.131559i | \(0.958002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.80311e7i | 2.55292i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.63020e6 | + | 1.03712e6i | 0.328108 | + | 0.0937381i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.99951e6 | 0.807245 | 0.403622 | − | 0.914926i | \(-0.367751\pi\) | ||||
0.403622 | + | 0.914926i | \(0.367751\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.10916e6 | −0.0987392 | −0.0493696 | − | 0.998781i | \(-0.515721\pi\) | ||||
−0.0493696 | + | 0.998781i | \(0.515721\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.12781e6 | + | 2.23344e7i | −0.276348 | + | 1.97329i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 8.43189e6i | − | 0.739385i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.15823e6i | 0.100805i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 680300. | − | 4.85774e6i | 0.0587673 | − | 0.419632i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.76794e7 | 3.23070 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.74919e6 | −0.148867 | −0.0744335 | − | 0.997226i | \(-0.523715\pi\) | ||||
−0.0744335 | + | 0.997226i | \(0.523715\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.22410e7 | + | 5.42865e6i | 1.03409 | + | 0.458598i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.67923e7i | − | 1.40812i | −0.710143 | − | 0.704058i | \(-0.751370\pi\) | ||
0.710143 | − | 0.704058i | \(-0.248630\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.34860e6i | − | 0.112256i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.90000e6 | − | 966309.i | −0.570140 | − | 0.0798451i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.94379e7 | 1.59440 | 0.797201 | − | 0.603714i | \(-0.206313\pi\) | ||||
0.797201 | + | 0.603714i | \(0.206313\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.01146e7 | 0.823614 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.06642e6 | − | 1.12966e6i | −0.652062 | − | 0.0913178i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.57251e7i | − | 1.26196i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 9.94513e6i | − | 0.792347i | −0.918176 | − | 0.396173i | \(-0.870338\pi\) | ||
0.918176 | − | 0.396173i | \(-0.129662\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.35171e6 | − | 1.52321e7i | 0.344213 | − | 1.20484i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.46007e7 | −1.14660 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.34797e7 | −2.61035 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.31232e6 | − | 1.65113e7i | 0.179001 | − | 1.27817i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.96927e6i | 0.151360i | 0.997132 | + | 0.0756798i | \(0.0241127\pi\) | ||||
−0.997132 | + | 0.0756798i | \(0.975887\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.06131e6i | 0.538886i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.71130e6 | − | 2.65009e7i | 0.281225 | − | 2.00811i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.49593e6 | 0.187795 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.75807e7 | 1.31347 | 0.656736 | − | 0.754121i | \(-0.271937\pi\) | ||||
0.656736 | + | 0.754121i | \(0.271937\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.85491e6 | − | 9.99296e6i | 0.211796 | − | 0.741344i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7.82163e6i | − | 0.576200i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.86220e7i | 2.82533i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.67092e7 | + | 2.34003e6i | 1.21383 | + | 0.169990i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.74937e7 | −1.98340 | −0.991700 | − | 0.128572i | \(-0.958961\pi\) | ||||
−0.991700 | + | 0.128572i | \(0.958961\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.26980e7 | 0.909695 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.75209e6 | + | 805549.i | 0.409242 | + | 0.0573121i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.31229e6i | 0.0927221i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.98468e7i | 1.39269i | 0.717706 | + | 0.696346i | \(0.245192\pi\) | ||||
−0.717706 | + | 0.696346i | \(0.754808\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.63239e6 | + | 1.06352e7i | 0.671298 | + | 0.741188i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.50135e7 | −1.73133 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.78657e7 | −1.22818 | −0.614088 | − | 0.789238i | \(-0.710476\pi\) | ||||
−0.614088 | + | 0.789238i | \(0.710476\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.48011e6 | − | 1.05689e7i | 0.101059 | − | 0.721623i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.75698e7i | 1.19151i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.32601e6i | − | 0.0893172i | −0.999002 | − | 0.0446586i | \(-0.985780\pi\) | ||
0.999002 | − | 0.0446586i | \(-0.0142200\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.62159e6 | + | 1.15791e7i | −0.108492 | + | 0.774693i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.81899e6 | 0.453156 | 0.226578 | − | 0.973993i | \(-0.427246\pi\) | ||||
0.226578 | + | 0.973993i | \(0.427246\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.79908e7 | −2.50777 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.79906e6 | + | 1.94244e6i | 0.445808 | + | 0.127364i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 4.43780e6i | − | 0.289044i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.64460e6i | 0.106405i | 0.998584 | + | 0.0532024i | \(0.0169428\pi\) | ||||
−0.998584 | + | 0.0532024i | \(0.983057\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.37187e7 | − | 1.92123e6i | −0.881710 | − | 0.123479i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.62027e6 | −0.422677 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.33078e7 | 0.844050 | 0.422025 | − | 0.906584i | \(-0.361319\pi\) | ||||
0.422025 | + | 0.906584i | \(0.361319\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.42243e7 | − | 4.79293e6i | −2.15640 | − | 0.301993i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.10386e7i | 1.31690i | 0.752623 | + | 0.658452i | \(0.228789\pi\) | ||||
−0.752623 | + | 0.658452i | \(0.771211\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 311178.i | 0.0193507i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.14176e7 | − | 1.18327e7i | −2.55877 | − | 0.731021i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.91463e6 | 0.178894 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.69563e7 | −1.03399 | −0.516993 | − | 0.855990i | \(-0.672949\pi\) | ||||
−0.516993 | + | 0.855990i | \(0.672949\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.78633e6 | + | 1.98960e7i | −0.168810 | + | 1.20540i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.16231e7i | − | 0.699635i | −0.936818 | − | 0.349817i | \(-0.886244\pi\) | ||
0.936818 | − | 0.349817i | \(-0.113756\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 8.86194e6i | − | 0.529999i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.24384e6 | − | 8.88177e6i | 0.0739117 | − | 0.527773i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.73573e7 | −1.02480 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.92166e7 | 1.12733 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −570070. | + | 1.28544e6i | −0.0332295 | + | 0.0749288i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.70850e6i | 0.504393i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.57942e6i | 0.436214i | 0.975925 | + | 0.218107i | \(0.0699881\pi\) | ||||
−0.975925 | + | 0.218107i | \(0.930012\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.83184e6 | − | 1.23685e6i | −0.505078 | − | 0.0707335i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.14024e6 | 0.292107 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.53207e7 | 1.99456 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.97445e7 | + | 4.16555e6i | 1.66912 | + | 0.233752i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 8.62153e6i | − | 0.480771i | −0.970677 | − | 0.240386i | \(-0.922726\pi\) | ||
0.970677 | − | 0.240386i | \(-0.0772739\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.56891e7i | 2.53189i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.24947e6 | + | 4.37349e6i | −0.0688091 | + | 0.240850i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.10394e7 | −0.604168 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.33620e7 | 1.27063 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.03273e6 | + | 3.59366e7i | −0.272032 | + | 1.94246i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.09025e6i | 0.327163i | 0.986530 | + | 0.163581i | \(0.0523046\pi\) | ||||
−0.986530 | + | 0.163581i | \(0.947695\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.47569e7i | 0.787849i | 0.919143 | + | 0.393925i | \(0.128883\pi\) | ||||
−0.919143 | + | 0.393925i | \(0.871117\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.65736e6 | − | 3.32563e7i | 0.247123 | − | 1.76460i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.28300e6 | −0.0676599 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.29681e7 | −0.679705 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.07931e6 | − | 1.42787e7i | 0.212509 | − | 0.743837i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.26636e6i | 0.0655689i | 0.999462 | + | 0.0327845i | \(0.0104375\pi\) | ||||
−0.999462 | + | 0.0327845i | \(0.989563\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.36418e7i | − | 1.21669i | −0.793672 | − | 0.608346i | \(-0.791833\pi\) | ||
0.793672 | − | 0.608346i | \(-0.208167\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.87763e7 | − | 5.43042e6i | −1.98350 | − | 0.277778i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.79378e6 | 0.243733 | 0.121867 | − | 0.992546i | \(-0.461112\pi\) | ||||
0.121867 | + | 0.992546i | \(0.461112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.79432e7 | 0.906802 | 0.453401 | − | 0.891307i | \(-0.350211\pi\) | ||||
0.453401 | + | 0.891307i | \(0.350211\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.30473e6 | + | 1.02299e6i | 0.366946 | + | 0.0513888i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.82214e7i | 0.909848i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 411285.i | − | 0.0204139i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.84972e6 | − | 8.68069e6i | 0.189939 | − | 0.428292i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.39791e7 | 1.66651 | 0.833253 | − | 0.552892i | \(-0.186476\pi\) | ||||
0.833253 | + | 0.552892i | \(0.186476\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.03733e7 | 0.993281 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.07523e6 | + | 2.19589e7i | −0.149042 | + | 1.06424i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.90350e6i | 0.284425i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.15444e7i | 1.51083i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.40830e6 | − | 3.14778e7i | 0.209895 | − | 1.49877i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.95646e7 | −0.926077 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.85782e6 | 0.181539 | 0.0907693 | − | 0.995872i | \(-0.471067\pi\) | ||||
0.0907693 | + | 0.995872i | \(0.471067\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.14727e7 | − | 6.13458e6i | −1.00455 | − | 0.286992i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 8.53164e6i | − | 0.396808i | −0.980120 | − | 0.198404i | \(-0.936424\pi\) | ||
0.980120 | − | 0.198404i | \(-0.0635758\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 7.87397e6i | − | 0.364092i | −0.983290 | − | 0.182046i | \(-0.941728\pi\) | ||
0.983290 | − | 0.182046i | \(-0.0582719\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.18322e7 | + | 3.05748e6i | 1.00367 | + | 0.140558i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.31086e7 | −0.599141 | −0.299570 | − | 0.954074i | \(-0.596843\pi\) | ||||
−0.299570 | + | 0.954074i | \(0.596843\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.45054e7 | 0.659160 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.09154e7 | + | 7.13043e6i | 2.30039 | + | 0.322157i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.03885e7i | 1.36509i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.64700e7i | 0.735612i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.43434e6 | − | 981166.i | −0.152513 | − | 0.0435719i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.07035e6 | 0.135571 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.26413e7 | 1.43307 | 0.716536 | − | 0.697550i | \(-0.245727\pi\) | ||||
0.716536 | + | 0.697550i | \(0.245727\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.71167e6 | − | 3.36440e7i | 0.205685 | − | 1.46871i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.98226e7i | − | 0.860443i | −0.902723 | − | 0.430221i | \(-0.858436\pi\) | ||
0.902723 | − | 0.430221i | \(-0.141564\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.27609e7i | − | 1.41401i | −0.707207 | − | 0.707007i | \(-0.750045\pi\) | ||
0.707207 | − | 0.707007i | \(-0.249955\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −772082. | + | 5.51312e6i | −0.0331364 | + | 0.236613i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.48920e7 | −1.48907 | −0.744537 | − | 0.667581i | \(-0.767330\pi\) | ||||
−0.744537 | + | 0.667581i | \(0.767330\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.37171e6 | 0.227960 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.56242e7 | − | 2.21642e7i | −1.50332 | − | 0.935313i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.36872e7i | 0.993998i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.96104e7i | − | 0.818330i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.20820e7 | − | 4.49291e6i | −1.33131 | − | 0.186443i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 930604. | 0.0384030 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.12813e7 | −2.10449 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.63113e7 | + | 2.28432e6i | 0.665687 | + | 0.0932259i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.67556e7i | 1.89763i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.81630e7i | − | 0.733111i | −0.930396 | − | 0.366555i | \(-0.880537\pi\) | ||
0.930396 | − | 0.366555i | \(-0.119463\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.81590e6 | − | 6.35615e6i | 0.0728926 | − | 0.255144i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.36338e7 | 1.34270 | 0.671352 | − | 0.741139i | \(-0.265714\pi\) | ||||
0.671352 | + | 0.741139i | \(0.265714\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.06759e7 | −0.820896 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.35642e6 | + | 6.68102e7i | −0.369451 | + | 2.63809i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.15144e7i | 1.23762i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.72283e7i | 0.672906i | 0.941700 | + | 0.336453i | \(0.109227\pi\) | ||||
−0.941700 | + | 0.336453i | \(0.890773\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.50316e6 | − | 1.07334e7i | 0.0583923 | − | 0.416955i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.80137e7 | 0.695984 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.21668e7 | −0.851821 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.23834e6 | − | 3.23367e7i | 0.353098 | − | 1.23594i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.18690e7i | − | 0.451207i | −0.974219 | − | 0.225603i | \(-0.927565\pi\) | ||
0.974219 | − | 0.225603i | \(-0.0724353\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.44676e6i | 0.357198i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 187409. | + | 26245.7i | 0.00704835 | + | 0.000987083i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.25951e8 | 4.71164 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.80420e7 | 0.671329 | 0.335664 | − | 0.941982i | \(-0.391039\pi\) | ||||
0.335664 | + | 0.941982i | \(0.391039\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.87292e6 | − | 1.10256e6i | −0.291388 | − | 0.0408073i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.10812e7i | 0.776107i | 0.921637 | + | 0.388053i | \(0.126852\pi\) | ||||
−0.921637 | + | 0.388053i | \(0.873148\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.80915e7i | − | 1.76112i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.59279e7 | + | 1.14985e7i | 0.944470 | + | 0.418854i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.72764e6 | −0.207539 | −0.103770 | − | 0.994601i | \(-0.533090\pi\) | ||||
−0.103770 | + | 0.994601i | \(0.533090\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.03484e7 | −0.372999 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.22110e6 | + | 3.01411e7i | −0.151347 | + | 1.08071i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.09351e7i | 1.10336i | 0.834054 | + | 0.551682i | \(0.186014\pi\) | ||||
−0.834054 | + | 0.551682i | \(0.813986\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2.79581e7i | − | 0.991972i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 570255. | − | 4.07195e6i | 0.0201275 | − | 0.143722i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.13715e7 | 0.399275 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.23447e7 | 0.780489 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.13013e7 | − | 3.22870e6i | −0.392703 | − | 0.112192i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.38853e7i | 2.20842i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.89231e7i | − | 1.33857i | −0.743006 | − | 0.669285i | \(-0.766600\pi\) | ||
0.743006 | − | 0.669285i | \(-0.233400\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.77608e7 | + | 5.28820e6i | 1.29191 | + | 0.180925i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.31321e6 | −0.248920 | −0.124460 | − | 0.992225i | \(-0.539720\pi\) | ||||
−0.124460 | + | 0.992225i | \(0.539720\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.64150e7 | −0.555852 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.63490e7 | − | 5.09049e6i | −1.22456 | − | 0.171494i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 7.25205e6i | − | 0.243066i | −0.992587 | − | 0.121533i | \(-0.961219\pi\) | ||
0.992587 | − | 0.121533i | \(-0.0387810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.32998e7i | − | 0.443494i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 792447. | + | 226396.i | 0.0262904 | + | 0.00751097i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.95103e7 | −1.63422 | −0.817112 | − | 0.576479i | \(-0.804426\pi\) | ||||
−0.817112 | + | 0.576479i | \(0.804426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.47740e7 | 1.47040 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.17249e6 | − | 2.97940e7i | 0.136333 | − | 0.973499i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3.59303e7i | − | 1.16807i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.25306e7i | − | 0.405311i | −0.979250 | − | 0.202655i | \(-0.935043\pi\) | ||
0.979250 | − | 0.202655i | \(-0.0649571\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.17321e6 | − | 2.26585e7i | 0.102123 | − | 0.729220i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.11415e7 | −1.63763 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.84608e7 | −0.588183 | −0.294092 | − | 0.955777i | \(-0.595017\pi\) | ||||
−0.294092 | + | 0.955777i | \(0.595017\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.17134e7 | − | 9.62947e6i | −0.688358 | − | 0.305273i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.6.c.a.383.1 | ✓ | 20 | |
3.2 | odd | 2 | 384.6.c.d.383.19 | yes | 20 | ||
4.3 | odd | 2 | 384.6.c.d.383.20 | yes | 20 | ||
8.3 | odd | 2 | 384.6.c.b.383.1 | yes | 20 | ||
8.5 | even | 2 | 384.6.c.c.383.20 | yes | 20 | ||
12.11 | even | 2 | inner | 384.6.c.a.383.2 | yes | 20 | |
24.5 | odd | 2 | 384.6.c.b.383.2 | yes | 20 | ||
24.11 | even | 2 | 384.6.c.c.383.19 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.c.a.383.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
384.6.c.a.383.2 | yes | 20 | 12.11 | even | 2 | inner | |
384.6.c.b.383.1 | yes | 20 | 8.3 | odd | 2 | ||
384.6.c.b.383.2 | yes | 20 | 24.5 | odd | 2 | ||
384.6.c.c.383.19 | yes | 20 | 24.11 | even | 2 | ||
384.6.c.c.383.20 | yes | 20 | 8.5 | even | 2 | ||
384.6.c.d.383.19 | yes | 20 | 3.2 | odd | 2 | ||
384.6.c.d.383.20 | yes | 20 | 4.3 | odd | 2 |